Mankind, probably throughout all its history, has tried to understand the world. In these attempts, the concept of the world itself has often changed. For thousands of years there had been countless descriptions—driven by religious, philosophical, nationalistic, artistic, even personal, beliefs—about its origins, features, structure, fate. But only in the early twentieth century a way to give to these descriptions more solid physical-mathematical bases was found. It was Albert Einstein who in 1917 explained, using his general theory of relativity, how to give a physical sense to the studies regarding the world in its entirety, i.e. the universe. Though the universe as a whole is not, and probably will never be, accessible empirically—the observable universe is in fact not the same as the entire universe—the new conception of physical cosmology introduced by Einstein, and named modern cosmology, is concerned exactly with that entity, the largest ever conceived in a science. But what exactly is the universe?
It is not easy to state a univocal definition. We can loosely define it as everything that has physical existence (subjected, at least in principle, to scientific analysis) in space and time, including spacetime itself. However, neither phenomena beyond the power of physics, such as thoughts and human emotions, nor small scale objects, such as atoms, birds, planets, are of interest to modern cosmology. It indeed studies only the large-scale features (typically of galactic or extra-galactic magnitude) of the universe, its physical structure and composition (the geometrical structure of space and the matter and radiation distributed in it), its topology, dynamics, evolution over time and its ultimate fate. In a few words, it focuses on the natural laws that govern the universe.
The main goal of my talk is to expound in which sense cosmologists speak of “worlds” or “universes”. As said, cosmologists are interested in comprehending as accurately as possible our universe. However, in doing so, they also need to study other possible universes, not necessarily consistent with our physical laws, in order to carry out comparisons and evaluate if the properties of our universe could have been otherwise. In other words, cosmologists try to understand why our universe has some properties and not others. In this way they “create” and investigate other hypothetical universes where the physical characteristics are different from those that are obtained in the real universe in which we live. How is it possible to produce exemplars of other universes? Once it is assumed that the structure of our universe is described by a solution of certain equations (the Einstein field equations), it follows that all other solutions describe other possible universes. Moreover, with the aid of supercomputers, some types of these virtual universes can be simulated. However, it is not an easy task to solve those equations, but the important point is that their solutions give global descriptions of spacetime as a whole, namely they allow to depict different kinds of universes, so giving an astounding powerful opportunity to human knowledge. I will discuss some of them, such as: rotating universes, empty universes, expanding and contracting universes, universes that allow time travels, cyclical universes, closed universes, eternal universes, etc. The exciting—and probably impossible, but… who knows?—challenge resides in understanding to what degree they are just mathematical fictional worlds or instead “places” actually existent somewhere out there in that hypothetical scenario contemplating innumerable universes usually called multiverse.